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Often you will want to cycle through the elements in a collection For example, you might want to display each element One way to do this is to use a foreach loop, as the preceding examples have done Another way is to use an enumerator An enumerator is an object that implements either the non-generic IEnumerator or the generic IEnumerator<T> interface IEnumerator defines one property called Current The non-generic version is shown here: object Current { get; } For IEnumerator<T>, Current is declared like this: T Current { get; } In both cases, Current obtains the current element being enumerated Since Current is a read-only property, an enumerator can only be used to retrieve, but not modify, the objects in a collection IEnumerator defines two methods The first is MoveNext( ): bool MoveNext( ) Each call to MoveNext( ) moves the current position of the enumerator to the next element in the collection It returns true if the next element is available, or false if the end of the collection has been reached Prior to the first call to MoveNext( ), the value of Current is undefined (Conceptually, prior to the first call to MoveNext( ), the enumerator refers to the nonexistent element that is just before the first element Thus, you must call MoveNext( ) to move to the first element) You can reset the enumerator to the start of the collection by calling Reset( ), shown here: void Reset( )

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After calling Reset( ), enumeration will again begin at the start of the collection Thus, you must call MoveNext( ) before obtaining the first element In IEnumerator<T>, the methods MoveNext( ) and Reset( ) work in the same way Two other points: First, you cannot use an enumerator to change the collection that is being enumerated Thus, enumerators are read-only relative to the collection Second, any change to the collection under enumeration invalidates the enumerator

Before you can access a collection through an enumerator, you must obtain one Each of the collection classes provides a GetEnumerator( ) method that returns an enumerator to the start of the collection Using this enumerator, you can access each element in the collection, one element at a time In general, to use an enumerator to cycle through the contents of a collection, follow these steps: 1 Obtain an enumerator to the start of the collection by calling the collection s GetEnumerator( ) method 2 Set up a loop that makes a call to MoveNext( ) Have the loop iterate as long as MoveNext( ) returns true 3 Within the loop, obtain each element through Current Here is an example that implements these steps It uses an ArrayList, but the general principles apply to any type of collection, including the generic collections

When we learned the theory of the integral, we found that the basic idea was that one can calculate the area of an irregularly shaped region by subdividing the region into rectangles We put the word rectangle here in quotation marks because the region is not literally broken up into rectangles; the union of the rectangles differs from the actual region under consideration by some small errors (see Figure 81) But the contribution made by these errors vanishes as the mesh of the rectangles become finer and finer We will now implement this same philosophy to calculate certain volumes Some of these will be volumes that you have heard about (eg, the sphere or cone), but have never known why the volume had the value that it had Others will be entirely new (eg, the paraboloid of revolution) We will again use the method of slicing

// Demonstrate an enumerator using System; using SystemCollections; class EnumeratorDemo { static void Main() { ArrayList list = new ArrayList(1); for(int i=0; i < 10; i++) listAdd(i); // Use enumerator to access list IEnumerator etr = listGetEnumerator(); while(etrMoveNext()) ConsoleWrite(etrCurrent + " "); ConsoleWriteLine(); // Re enumerate the list etrReset(); while(etrMoveNext()) ConsoleWrite(etrCurrent + " "); ConsoleWriteLine(); } }

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Imagine a solid object situated as in Figure 82 Observe the axes in the diagram, and imagine that we slice the figure with slices that are vertical (ie, that rise out of the x-y plane) and that are perpendicular to the x-axis (and parallel to the y-axis) Look at Figure 83 Notice, in the figure, that the figure extends from x = a to x = b If we can express the area of the slice at position x as a function A(x) of x, then (see Figure 84) the volume of a slice of thickness x at position x will be

0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9

In general, when you need to cycle through a collection, a foreach loop is more convenient to use than an enumerator However, an enumerator gives you a little extra control by allowing you to reset the enumerator at will